Electrical detection and modulation of magnetism in a Dy-based ferroelectric single-molecule magnet

Electrical control of magnetism in single-molecule magnets with peculiar quantum magnetic behaviours has promise for applications in molecular electronics and quantum computing. Nevertheless, such kind of magnetoelectric effects have not been achieved in such materials. Herein, we report the successful realization of significant magnetoelectric effects by introducing ferroelectricity into a dysprosium-based single-molecule magnet through spatial cooperation between flexible organic ligands and halide ions. The stair-shaped magnetization hysteresis loop, alternating current susceptibility, and magnetic relaxation can be directly modulated by applying a moderate electric field. Conversely, the electric polarization can be modulated by applying a small magnetic field. In addition, a resonant magnetodielectric effect is clearly observed, which enables detection of quantum tunnelling of magnetization by a simple electrical measurement. The integration of ferroelectricity into single-molecule magnets not only broadens the family of single-molecule magnets but also makes electrical detection and modulation of the quantum tunnelling of magnetization a reality.


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E-field control of temperature-dependent AC magnetic susceptibility (Supplementary Fig. 19) E-field control of frequency-dependent AC magnetic susceptibility (Supplementary Fig. 20) Magnetic relaxation analyses under E-field (Supplementary Fig. 21) E-field control of magnetization relaxation time at 2 K (Supplementary Fig. 22) Magnetization relaxation time at different temperatures without E-field (Supplementary Fig. 23)

Excluding heating effect with applied electric fields•••••••••••••••pages 32-34
Discussions on excluding heating effect Sample temperature fluctuations as the E-field off and on (Supplementary Fig. 24) E-field control of M−H loops with ITO films (Supplementary Fig. 25) Crystallographic data and structural refinements (Supplementary Table 1) Continuous shape measure calculated values (Supplementary Table 2) Magnetic relaxation fitting results for a powder sample (Supplementary Table 3) Magnetic relaxation fitting results for a single-crystal sample (Supplementary Tables 4-5) SA-CASSCF/RASSI-calculated electronic states (Supplementary Table 6) Magnetic relaxation fitting results for a single-crystal sample under E-fields (Supplementary Table 7) 1. Basic characterization Supplementary Fig. 1 | Photographs of single crystals.a, the representative crystals with size scales.b, the (0-11) plane, as determined by single-crystal X-ray diffraction.

Additional crystal structure descriptions
Variable-temperature crystal structures illustrated a structural transition.At 300 K, one crystalline-independent Dy 3+ ion was observed in each symmetric unit, with two coordinated ligands in opposite directions, five coordinated water molecules in the equatorial plane, three Cl − ions, one water molecule and one acetonitrile molecule in the outer coordination sphere (Supplementary Fig. 3).
The average bond lengths of the three nearby diagonal substituent groups at 50 K were found to be equal to the corresponding bond lengths at 300 K, causing the c glide planes to vanish.The differences between the structures at 300 and 50 K are similar to those between the two conformational isomers, and the slight lengthening or shortening of the bonds rather than significant displacement is mainly due to the steric hindrance of the ligand.
The coordination environment of the Dy 3+ ion was found to be a slightly distorted pentagonal bipyramid with average Dy-O distances of 2.206(1) Å (axial) and 2.376(4) Å (equatorial) and an axial O-Dy-O angle of 173.10(13) (Supplementary Table 1).Continuous shape measure (CSM) calculations were carried out on the DyO7 sites.The minimum deviation from an ideal model of the D5h geometry indicated that the Dy 3+ ion was situated within a slightly distorted pentagonal bipyramid coordination environment at both 300 K and 50 K (Supplementary Table 2).Therefore, Dy-SMM is expected to have high-performance SMM properties due to exhibiting the appropriate uniaxial anisotropy.

Ab initio calculations
Ab initio calculations were performed at the SA-CASSCF/RASSI level to predict the electronic structure of Dy-SMM.The structures obtained with the XRD analysis were employed directly without any optimization in the theoretical calculations.The results showed that the ground state doublet was a pure |±15/2> state (99.3%).
Furthermore, the gz value close to 20 was observed to be almost collinear with the two shortest chemical bonds of the Dy ion (g is the Landau factor).The energy of the first excited state was 504 K higher than that of the ground state (98.5% |±13/2> state).
The deviation angle of gz in this state relative to the gz of the ground Kramers doublet was only 3.4°, still quite close to the pseudo-C5 axis.The second excited state was at 677 K above the ground state with a highly mixed wavefunction of 39.7%|±1/2> + 35.9%| ∓ 1/2> + 15.1%|±3/2>.The g tensor contained a significant transverse component (gx = 0.52, gy = 1.91, gz = 17.87), and the gz axis was almost perpendicular to the gz of the ground Kramers doublet (89.6°).Therefore, the magnetic relaxation through the Orbach process likely proceeded via the second excited state, giving a calculated energy barrier of 677 K, which agrees well with the experimentally determined value of 643 K.The small values of the coefficient α (< 0.17) under the application of a magnetic field (H) both perpendicular and parallel to the (0-11) plane (Supplementary Fig. 8 and Supplementary Tables 4 and 5) indicated a narrow distribution for the relaxation time (τ).The best fitting results showed that ln(τ) was inversely proportional to T, indicating that the thermally activated Orbach process was dominant in the higher temperature range (29−40 K).In the lower temperature range (10−28 K), however, the temperature-dependent relaxation tended to obey the power law τ ~T−n instead, presumably due to the involvement of the Raman process below 29 K (as is commonly observed in SMMs with extremely long relaxation times).

Magnetic relaxation processes of the single-crystal sample of
By including the equations of the Orbach and Raman relaxation processes, the temperature dependent relaxation time plots were described well by τ −1 = τ0 −1 exp(−Ueff/kBT) + CT n (τ0 is the preexponential factor, Ueff is the effective energy barrier, C and n are constant parameter values of the Raman process that do not have a physical basis, and kB is the Boltzmann constant) over the whole temperature range.

Excluding heating effect with applied electric fields
One may argue that the induced magnetism change could be due to a thermal heating effect when an E-field is applied to the sample.We have safely excluded the heating effect due to the following reasons.Firstly, the multiferroic SMM is highly insulating, with a resistance of ~10 14 ohm and a loss tangent of ~0.002 at low temperatures.The applied E-fields of several kV/cm only generate a tiny current of 10 -11 ampere at 2 K. Secondly, we monitored the sample temperature through a Cernox thin film resistance temperature sensor placed near the sample during the magnetization measurements, and observed a maximum temperature fluctuation of approximately 0.006 K (Supplementary Fig. 24).This is far below the temperature change that would be necessary to produce heat-induced changes in magnetization.
Thirdly, we performed a control experiment by placing the sample between two parallel conductive indium tin oxide (ITO) films without electrical contact with the sample.There is no current passing through the sample so that the heating effect can be completely avoided.The ME effect obtained in this non-contacting method is similar to that using the contacting electrodes (Supplementary Fig. 25).There are also other issues to exclude the heating effect.For example, both the magnetic coercivity and remanent magnetization were reduced by the applied E-field, but the saturation magnetization is almost unchanged.The strongly anisotropic behaviour of E-field control of magnetization also suggests that the observed ME effect is intrinsic to the multiferroic SMM.method of applying electric fields between two indium-tin oxide (ITO) films without direct contact with the sample.This method aims to eliminate any possible heating effect.b, The sample was cooled from 300 to 2 K.When the temperature was stable at 2 K, the M-H loop without an E-field (E = 0 kV/cm) was first collected.Then, the M-H loops with E fields of 3.3 kV/cm and 4.2 kV/cm were measured.The ME effect measured in this way is similar to that using the contacting silver paste electrodes.
Note: The single-crystal data collected at 200 K in the X-ray diffraction experiment are different from the electrical measurements obtained with the PPMS.The discrepancy could be due to temperature inaccuracy in the single-crystal X-ray diffraction experiments.Because a large cavity is needed to permit CCD operation, the actual temperature of the sample could be well below the controlling temperature, and a long time is required to reach thermal equilibrium.

Supplementary
Temperature dependence of the AC magnetic susceptibility of Dy-SMM.a,b Temperature dependence of the in-phase (χ′) and out-of-phase (χ″) components of the AC magnetic susceptibility of a powder sample.c-f Temperature dependence of the in-phase (χ′) and out-of-phase (χ″) components of the AC magnetic susceptibility of a single-crystal sample with a magnetic field applied (c,d) perpendicular and (e,f) parallel to the (0-11) plane.
Dy-SMM were investigated through fitting the Cole-Cole plot by the generalized Debye model and fitting the temperature dependent relaxation time plot by the equation including of the Orbach and Raman relaxation processes.

Table 1 |
Crystallographic data and structural refinements for

Table 3 |
Best fit results using the generalized Debye model for a

Table 4 |
Best fit results using the generalized Debye model for the magnetic relaxations with the magnetic field perpendicular to the (0-11) plane for a single crystal sample of Dy-SMM.

Table 5 |
Best fitting results using the generalized Debye model for the magnetic relaxations with the magnetic field parallel to the (0-11) plane for a single crystal sample of Dy-SMM.

Table 7 |
Best fitting results obtained using the generalized Debye model for the magnetic relaxations with magnetic and electric fields perpendicular to the (0-11) plane for a single crystal of Dy-SMM under an electric field.